Chapter 8.6, Problem 12WE

To determine

To find: The value of the variables x and y.

Answer to Problem 12WE

  $x=20,y\approx 10$

Explanation of Solution

Given information:

Calculation:

The two angles of the triangle are $30°,75°$ .

Then, the third angle is $180°-(30°+75°)=180°-105°=75°$ .

Since, two angles of the triangle are $75°$ , the angle is isosceles.

Then, the two sides of the triangle are equal.

  $\therefore x=20$

Let, a median of the triangle be drawn as shown in the figure below,

Using Trigonometric ratios,

  $\begin{array}{l}\cos 75°=\frac{\frac{y}{2}}{20}\\ \Rightarrow \cos 75°=\frac{y}{40}\\ \Rightarrow y=40\times \cos 75°\\ \Rightarrow y\approx 40\times 0.2588[\because \cos 75°\approx 0.2588]\\ \Rightarrow y\approx 10.352\text{ or }10\end{array}$

Thus, $y\approx 10$